For the BLG ribbon with the edge configuration shown in Fig. REF ,
there is no edge state even if non-zero \(U\)  and \(\gamma _{3}\)  are
considered. For the other edge configuration as shown in Fig. REF ,
the edge states which are gapped and flat appear when non-zero interlayer
bias is added. Here we would like to point out that these edge states are
not topological for three reasons: (i) They cannot be described by the
bulk-edge correspondence we used before since their energy is not at the
Fermi level. (ii) They are not robust since they disappear when including \(\gamma _{3}\) , the quantity that preserves original chiral symmetry of the
system and do not influence the existence of edge states in the case of
bilayer bearded-bearded (zigzag-zigzag) ribbon (discussed below). (iii) Most
importantly, they are not formed between two Dirac points with different
topological charges [1]}, [2]}, [3]}, [4]} in the band structure. But this
fact is still interesting since it indicates the existence of edge states
can be determined by interlayer bias.
<FIGURE>